Finite Group Databasebeta

← #6763406

Subgroups — #6763406

Order 512.

1756 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic
3#33043C211yesmaximal, characteristic, complemented
4#31840C214yesmaximal, complemented
5#31640C214yesmaximal, complemented
6#30205C211yesmaximal, characteristic, complemented
7#29808C211yesmaximal, characteristic, complemented
8#29141C211yesmaximal, characteristic, complemented
9#28616C211yesmaximal, characteristic, complemented
10#27972C211yesmaximal, characteristic, complemented
11#27961C211yesmaximal, characteristic, complemented
12#25722C211yesmaximal, characteristic, complemented
13#25600C211yesmaximal, characteristic, complemented
14#24532C214yesmaximal, complemented
15#23970C214yesmaximal
16#22270C211yesmaximal, characteristic, complemented
17#21860C211yesmaximal, characteristic, complemented
18C2×#1956C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic
20C2×#554C2212yes—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#494C2211yescharacteristic
24C2×#494C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#451C2214yes—
27C2×#431C2211yescharacteristic
28C22×#103C2214yes—
29C22×C4×C8C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2567C2212yes—
37#2552—21no—
38#2552—21no—
39#2550—21no—
40#2502C2212yes—
41#2502C2212yes—
42#2492—21no—
43#2451—21no—
44#2446C2212yes—
45#2442—21no—
46#2440—21no—
47#2440—21no—
48#2440—21no—
49#2440—21no—
50#2439—21no—
51#2429C2212yes—
52#2417—21no—
53#2409C2212yes—
54#2360—21no—
55#2352—21no—
56D4×C4⋊C4—21no—
57D4×C4⋊C4—21no—
58Q8×C22⋊C4C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2100C2214yes—
65#2072C2214yes—
66#2072C2214yes—
67#2056C2214yes—
68#2056C2214yes—
69#2024C2214yes—
70#2024C2214yes—
71#2016C2214yes—
72#2001C2214yes—
73#2001C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2214yes—
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1933C2214yes—
86#1923C2212yes—
87#1916C2212yes—
88#1892C2214yes—
89#1878C2214yes—
90#1878C2214yes—
91#1878C2214yes—
92#1878C2214yes—
93#1872C2214yes—
94#1872C2214yes—
95#1869C2212yes—
96#1850C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1824C2214yes—
101#1803C2214yes—
102#1803C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C23×Q8C2312yes—
108C22×Q16C2314yes—
109C22×Q16C2314yes—
110C23×C8C2312yes—
111#554—48no—
112#533—24no—
113#533—42no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2312yes—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×#125—22no—
127C2×#125—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—22no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×C22⋊Q8C2312yes—
136C2×C4×Q8—21no—
137C2×C4×Q8C2312yes—
138C2×C4×Q8C2312yes—
139C2×C4×Q8C2312yes—
140C2×C4×D4—22no—
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×C4×D4C2311yescharacteristic
144C2×#117—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#494—24no—
156#494—42no—
157#487—42no—
158#451—48no—
159#431—42no—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#103—48no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C4×C8—42no—
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2312yes—
180#400—22no—
181#398—22no—
182#398—22no—
183#398—22no—
184#398—22no—
185#398—22no—
186#398—22no—
187#396—22no—
188#395—22no—
189#395—22no—
190#395—22no—
191#393—22no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—22no—
196#391—22no—
197#391C2312yes—
198#391C2312yes—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#391C2312yes—
204#389—22no—
205#389—22no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#388—22no—
220#387—22no—
221#387—22no—
222#386—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#384—21no—
229#384—21no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2312yes—
237#384C2312yes—
238#384C2312yes—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—22no—
251#380C2312yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4—22no—
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—24no—
282C22×Q8—28no—
283C22×Q8—42no—
284C22×Q8—44no—
285C22×Q8C2412yes—
286C22×Q8C2412yes—
287C22×Q8C2412yes—
288C22×D4C2×D411yescharacteristic
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×Q16—28no—
299C2×Q16—44no—
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×Q16—44no—
304C22×C8—24no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C4⋊Q8—24no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—44no—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8—42no—
323C4⋊Q8—82no—
324C4⋊Q8—82no—
325C4⋊Q8#4114yes—
326#125—44no—
327#125—48no—
328C22⋊Q8—24no—
329C22⋊Q8—28no—
330C22⋊Q8—48no—
331C22⋊Q8—48no—
332C22⋊Q8—42no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C4×Q8—24no—
338C4×Q8—42no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—48no—
345C4×D4Q1618yescomplemented
346#117—44no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—82no—
386C2×C4⋊C4—82no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4—82no—
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C4⋊C8—42no—
429C4⋊C8—42no—
430#103—44no—
431#103—44no—
432#103—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438C22⋊C8—24no—
439C22⋊C8—42no—
440C22⋊C8—42no—
441C4×C8—22no—
442C4×C8—22no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—42no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468C24C22×D411yescharacteristic
469C24C22×D411yescharacteristic
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—416no—
484C2×Q8—44no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—82no—
489C2×Q8—82no—
490C2×Q8—82no—
491C2×Q8—88no—
492C2×Q8C2×#4114yes—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4C2×Q1614yes—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4C2×Q1614yes—
530C22×C4C2×Q1614yes—
531C22×C4#13714yes—
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4H(5,𝔽2)14yes—
545C22×C4C2511yescharacteristic
546Q16—88no—
547Q16—88no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—48no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C2×Q1614yes—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—82no—
613C22⋊C4C2×Q1614yes—
614C22⋊C4C2×Q1614yes—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—22no—
627C42—22no—
628C42—44no—
629C42—44no—
630C42—82no—
631C42C2×Q1614yes—
632C42C2×#4112yes—
633C42H(5,𝔽2)12yes—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23#53512yes—
645C23C22×Q1612yes—
646C23C22×Q1612yes—
647C23C2×#13712yes—
648C23C23×D411yescharacteristic
649Q8—28no—
650Q8—44no—
651Q8—44no—
652Q8—44no—
653Q8—44no—
654Q8—44no—
655Q8—88no—
656Q8—84no—
657Q8—164no—
658D4—28no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—88no—
716C2×C4—164no—
717C2×C4—164no—
718C2×C4#53512yes—
719C2×C4#54612yes—
720C2×C4#54612yes—
721C2×C4C22×Q1612yes—
722C2×C4C22×Q1612yes—
723C2×C4C22×Q1612yes—
724C2×C4C22×Q1612yes—
725C2×C4C22×Q1612yes—
726C2×C4C2×#13712yes—
727C2×C4C2×#13712yes—
728C2×C4#57712yes—
729C2×C4#57712yes—
730C2×C4C22×#4111yescharacteristic
731C2×C4C2×H(5,𝔽2)12yes—
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4#58512yes—
734C8—42no—
735C8—42no—
736C8—42no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22#320914yes—
752C22C2×#53511yescharacteristic
753C22C2×#54611yescharacteristic
754C22#350011yescharacteristic
755C22C23×Q1611yescharacteristic
756C22C22×#13711yescharacteristic
757C22C2×#57711yescharacteristic
758C22C2×#57711yescharacteristic
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—44no—
769C4—41no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4#329914yes—
778C4#331614yes—
779C4#351312yes—
780C4#354212yes—
781C2—24no—
782C2—42no—
783C2#3808211yescharacteristic
784C2C2×#320911yescharacteristic
785C2#6081811yescharacteristic
786C2C2×#329911yescharacteristic
787C2C2×#331611yescharacteristic
788C2#6253011yescharacteristic
789C2#6254211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #33043C2semidirect
4. #31840C2semidirect
5. #31640C2semidirect
6. #30205C2semidirect
7. #29808C2semidirect
8. #29141C2semidirect
9. #28616C2semidirect
10. #27972C2semidirect
11. #27961C2semidirect
12. #25722C2semidirect
13. #25600C2semidirect
14. #24532C2semidirect
16. #22270C2semidirect
17. #21860C2semidirect
18. C2×#1956C2semidirect
345. C4×D4Q16semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#361802
#361292
#330432
#318402
#316402
#302052
#298082
#291412
#286162
#279722
#279612
#257222
#256002
#245322
#239702
#222702
#218602
C2×#19562
#211012